Senate Majority Leader Mitch McConnell plans to introduce legislation raising the minimum age to purchase tobacco products to 21 from 18, a move that public-health advocates and tobacco companies hope would curb the use of e-cigarettes among youths.

More than a dozen states have passed or enacted laws raising the minimum age to 21 and others are considering doing so. Sen. McConnell’s announcement Thursday follows the introduction earlier this month of similar bills in the House.

Altria Group Inc.
MO -3.69%
and
British American Tobacco
BTI -3.24%
PLC, the two biggest U.S. cigarette manufacturers, both support an increase of the minimum age to 21, as does Juul Labs Inc., a startup whose e-cigarettes are blamed by health officials for a surge in underage smoking.

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Laws raising the age to 21 “fight one of the largest contributors to this problem: sharing by legal-age peers,” Juul Chief Executive
Kevin Burns
said.

The increase has prompted a regulatory crackdown on the e-cigarette industry. The Food and Drug Administration in March issued new sales restrictions that will effectively ban convenience stores and gasoline stations from selling most flavored e-cigarettes. The passage of a bill raising the legal age nationwide to 21 could alleviate that regulatory pressure, analysts say.

“For some time, I’ve been hearing from the parents who are seeing an unprecedented spike in vaping among their teenage children,” Sen. McConnell said, adding that his bill would exempt military-service members. The Kentucky Republican said he would introduce his bill in May.

Altria, which makes Marlboro, has been lobbying for the move at the state and federal levels, last week taking out ads in The Wall Street Journal, the Washington Post and other news outlets. The tobacco giant has much at stake: In December, it invested $12.8 billion for a minority stake in Juul.

“This is the most effective action to reverse rising underage” use of e-cigarettes, Altria CEO
Howard Willard
said in a news release Thursday. According to the Food and Drug Administration, the most common way children and teens obtain e-cigarettes is from someone they know. Mr. Willard and other proponents of the policy change say a minimum age of 21 would ensure that high-school students wouldn’t have classmates who could purchase e-cigarettes for them.

Over the long term, a move to 21 could hasten the decline of cigarette sales. Among people who smoke cigarettes daily, 87% first used a cigarette by age 18, according to a 2014 Surgeon General report.

About 5% of adult tobacco consumers are between 18 and 20 years old, Ms. Kaufman said. She added that retailers estimated that a nationwide increase of the minimum age to 21 could cause tobacco sales to drop about 4% in the short term.

Shares of Altria and BAT fell 3.2% and 1.5%, respectively, in New York trading on Thursday.